Data Analysis

1. Researchers investigating crime believe that at least 40% of all arsonists are under 21 years of age. Checking local crime statistics, they found that 34 out of 80 arson suspects were under 21. a) What is the variable of interest of the researchers? b) Does the sample data support their belief? Perform an appropriate hypothesis test. c) If the researchers want to be 95% confident that the error of estimate to be within 0.05, what sample size is required for the study? 2. The average cholesterol content of a certain brand of eggs is 215 milligrams and the standard deviation is 15 milligrams. Assume that the cholesterol content in eggs is normally distributed. a) If a single egg is selected, find the probability that the cholesterol content will be more than 220 milligrams. b) For a random sample of size 25, state the sampling distribution of the sample mean. (Specify the name of the distribution and the parameters of the distribution.) c) If a random sample of 25 eggs is selected, find the probability that the cholesterol content will be more than 220 milligrams. 3. In order to test a theory that alcohol consumption can have an effect on test scores, a researcher conducted a study on 10 randomly selected adults. Each subject was given a test. Then for one week, each subject is required to consume a specific amount of alcohol, then they are tested again. Data on the test scores are given below. Subject Before Consumption After Consumption 1 105 106 2 109 105 3 98 95 4 112 109 5 109 105 6 117 115 7 123 125 8 114 114 9 95 98 10 101 100 Is there evidence that alcohol consumption has reduced the test score? a) Stating appropriate hypotheses, perform a parametric test and make conclusions in the context of the study. b)Stating appropriate hypotheses, 4. Researchers investigating crime believe that at least 40% of all arsonists are under 21years of age. Checking local crime statistics, they found that 34 out of 80 arson suspects were under 21. a) What is the variable of interest of the researchers? b) Does the sample data support their belief? Perform an appropriate hypothesis test. c) If the researchers want to be 95% confident that the error of estimate to be within 0.05, what sample size is required for the study?